Title:Heatline and entropy generation analysis on natural convection within containers of various shapes with identical fluid mass and heat input

Abstract

The shape of the enclosures plays a huge role for improving the thermal processing and heat transfer rates for various engineering applications.
In the present work, heat transport, thermal mixing and energy analysis of nine different enclosures of the same area (area= 1 sq. unit) and identical heating of the bottom wall (uniform/ non uniform) are categorized into three classes based on their geometric configuration [class 1 (square, tilted square – inclined at an angle of 450 with the X axis and parallelogram), class 2 (trapezoidal type 1, trapezoidal type 2 and triangle) and class 3 (convex, concave and right-angled triangle with curved hypotenuse)].
A detailed numerical analysis is performed for Rayleigh numbers (Ra) ranging from 103 to 105 for various Prandtl numbers (Pr = 0.025 and 155) via the Galerkin finite element method with penalty parameter.
Streamlines, heatlines and isotherms are used in order to analyse the fluid flow, heat flow and temperature distribution in all the enclosures.
Heat transfer rates are represented in terms of average Nusselt number.
In addition, the spatial average temperature is also determined.
Thermal mixing is higher in all the enclosures at Pr=155 compared to Pr=0.025.
Based on the optimal average Nusselt number and spatial average temperature which is essential for efficient thermal processing, the following enclosures are suitable for uniform heating [class 1: square, class 2: trapezoidal type 1 and class 3: convex] and non uniform heating [class 1: square, class 2: trapezoidal type 2 and class 3: convex].
Overall, it is found that heat transfer rates and spatial average temperature are higher during uniform heating leading to efficient thermal processing compared to the non uniform heating irrespective of Ra and Pr.